lssgb lesson3 measure

Copyright 2014, Simplilearn, All rights reserved.


Lesson 3Measure

Lean Six Sigma Green Belt


Explain process definition

Create X-Y diagrams

Describe types of statistics and statistical distributions

Collect and summarize data

Perform Measurement System Analysis (MSA)

Differentiate between precision and accuracy

Describe bias, linearity, and stability of measurements

Explain process capability

After completing this lesson, you will be able to:

Objectives

2


Measure

Topic 1Process Definition


Introduction to Measure Phase

The key objective of the measure phase is to gather as much

information as possible on the current processes.

The key tasks of the measure phase are:

creating a detailed process map;

gathering baseline data;

summarizing and analyzing the data;

performing Measurement Systems Analysis; and

performing process capability studies.

4


Process Mapping

Process mapping refers to a workflow diagram which gives a clear understanding of the process or a

series of parallel processes.

Process mapping can be done by using flowcharts, written procedures, or detailed work instructions.!

First step in process improvement

Gives wider perspective of the problems and opportunities

Provides a systematic way of recording

Features of process mapping

5


The X-Y diagram is a Six Sigma tool that helps in correlating Inputs (X) and Outputs (Y). It can be used

to identify what inputs are more valuable and impactful when there are multiple inputs and outputs

in a project.

X-Y Diagram

Steps to Create X-Y Diagram

Capture all the inputs and outputs variables.1

Insert an impact or correlation factor. 2

Provide the weightage of output (This explains how each of the input variable impacts what set of output variables).

3

After entering all the data, identify the inputs that are more valuable or impactful and take actions accordingly.

4

6


X-Y Diagram Template

List down each of the input variables.

List down each of the output variables.

Insert weight for each output.

Capture the impact value.

Use all the value from (b) for each of the input variable and multiply individually with the values given in (a), added value is (c).

The sample template of X-Y diagram is shown here.

1

2

3

4

5

a

b c

7


Measure

Topic 2 Descriptive and Inferential Statistics


Statistics refers to the science of collection, analysis, interpretation, and presentation of data. There

are two major types of statisticsDescriptive statistics and Inferential statistics.

Types of Statistics

Descriptive Statistics

Also known as Enumerative statistics

Includes organizing, summarizing, and

presenting the data

Describes what's going on in the data

Histograms, pie charts, box plots, etc., are

the tools

Inferential Statistics

Also known as Analytical statistics

Includes predicting and drawing conclusions

Makes inferences from our data to more

general conditions

Hypothesis testing, scattered diagram, etc.,

are the tools

9


Analytical Statistics

The main objective of statistical inference or analytical statistics is to draw conclusions on population

characteristics based on the information available in the sample. A sample from the population is

collected. An assessment about the population parameter is made from the sample.

The management team of a cricket council wants to know if the teams performance has improved after

recruiting a new coach. Is there a way the improvement can be proven statistically?Q

Here, Ya = Efficiency of Coach A and Yb = Efficiency of Coach B

a. Null HypothesisAssumption is Coach A and Coach B are both effective.

Assuming status quo is null hypothesis

H0: Ya = Ybb. Alternate HypothesisAssumption is the efficiencies of the two coaches differ.

If the null hypothesis is proven wrong, the alternate hypothesis must be right.

H1: Ya Yb

A

10


Central Limit Theorem (CLT) states that for a sample size greater than 30, the sample mean is very

close to the population mean.

When sample size is greater than 30, the sample mean approaches normal distribution.

In such cases, the Standard Error of Mean (SEM) that represents the variability between the

sample means is very less.

Central Limit Theorem

SEM =Population Standard Deviation

Sample Size

Selecting a sample size also depends on the concept called Power of the Test.!

11


The graphical representation of the Central Limit Theorem is given:

Central Limit TheoremGraph

12


The Central Limit Theorem concludes the following:

Sampling distributions are also helpful in dealing with non-normal data.

If the sample data points are taken from a population and the distribution of the means of samples

is plotted, it is called the sampling distribution of means.

This sampling distribution will approach normality as the sample size increases.

Central Limit TheoremConclusions

CLT aids in making inferences from the sample statistics about the population parameters irrespective of the distribution of the population.

CLT becomes the basis for calculating the confidence interval for a hypothesis test as it allows the use of a standard normal table.

!

13


Measure

Topic 3Collecting and Summarizing Data


Data is a collection of facts from which conclusions can be drawn. The two types of data are:

Types of Data

Attribute Data (Discrete)

Is countable and only includes integers such as 2, 40, 1050

Answers questions such as how many?, how often?, or what type?

Examples:

o Number of defective products

o Percentage of defective products

o Frequency of machine repair

o Type of award received

Variable Data (Continuous)

Can be measured and includes any real number such as 2.045, -4.42, or 45.65

Answers questions such as how long?, what volume?, or how far?

Examples:

o Height

o Weight

o Time taken to complete a task

15


The first step in the measure phase is to determine the type of data required based on the following

considerations:

Selecting Data Type

It is difficult to convert attribute data to variable data in the absence of assumptions or additional information, which can include retesting all units.!

Critical to Quality parameters (CTQs), Key Process Output Variables (KPOVs), and Key Process Input Variables (KPIVs)

What variables have been identified for the process?

The type of data that fits the metrics for the key variablesWhat type of data is selected?

Enables collecting, analyzing, and drawing inferences from the right set of data

Why should the data type be identified?

16


Simple Random Sampling vs. Stratified Sampling

Simple Random Sampling

Simple random sampling is easy to carry out.

Possibility of erroneous results is high.

This type of sampling cannot indicate possible causes of variation.

Stratified Sampling

Stratified sampling is time consuming and requires more effort.

Possibility of errors is minimized.

When done correctly, it is capable of showing assignable causes of variation.

The differences between simple random sampling and stratified sampling are given here.

17


A measure of central tendency is a single value that indicates the central point in a set of data. The

three most common measures of central tendency are as follows:

Descriptive StatisticsMeasures of Central Tendency

Mean Median Mode

Most common measure of central tendency

Given by the sum of entries in a data set and divided by the number of entries

Also called average or arithmetic mean

Also known as positional mean

Number in the middle of the data set

Mean of the middle two numbers in an even data set

Also calculated using:

Also known as frequency mean

Value that occurs most frequently in a data set

Median = +1

2

18


For the following data set, the mean, median, and mode are calculated:

Mean, Median, and ModeExample

1, 2, 3, 4, 5, 5, 6, 7, 8

Mean =1+2+3+4+5+5+6+7+8

9= 4.56

Median = 5

Mode = 5

19


The dataset is modified to include a new value. The new dataset is given:

The following observations can be made:

The new mean is 15.11.

Almost 90% of the values fall to the left of the mean.

The mean is skewed due to the presence of an extreme data point, 100, called an outlier.

The median of the dataset is unchanged at 5.

Mean, Median, and ModeOutliers

1, 2, 3, 4, 5, 6, 7, 8, 100

When the dataset has outliers, median is preferred over mean as a measure of central tendency.!20


Measures of dispersion describe the spread of values. Higher the variation of data points, higher the

spread of the data. The three main measures of dispersions are as follows:

Range

Variance

Standard Deviation

Descriptive StatisticsMeasures of Dispersion

21


Range is defined as the difference between the largest and smallest values of data.

For the data set given here,

the range is calculated as follows:

Measures of DispersionRange

4, 8, 1, 6, 6, 2, 9, 3, 6, 9

Range = Maximum Minimum

= 9 1

= 8

22


Variance is defined as the average of squared mean differences and shows the variation in a data set.

Consider the data set given here:

Sample variance can be calculated using the formula = VARS() in an Excel sheet. Population variance

can be calculated using the formula = VARP(). Here,

Sample variance = 8.04

Population variance = 7.24

Measures of DispersionVariance

Variance = 2 = ( )2

1

Variance is a measure of variation and cannot be considered as the variation in a data set. Population variance is preferred over sample variance as it is an accurate indicator of variation.!

4, 8, 1, 6, 6, 2, 9, 3, 6, 9

23


Measures of DispersionStandard Deviation

Standard deviation is given by the square root of variation.

For the same data set:

Population standard deviation = 2.69

(using the formula = STDEVP() in Excel)

Sample standard deviation = 2.83

(using the formula = STDEV() in Excel)

Standard Deviation = = ( )2

1

4, 8, 1, 6, 6, 2, 9, 3, 6, 9

Manual Method

Calculate mean.1

Calculate difference between each data point and the mean, square each answer.

2

Calculate the sum of the squares.

3

Divide the sum of the squares by N or n-1 (to find variance).

4

Find square root of variance.5

24


Frequency distribution is the grouping of data into mutually exclusive categories showing the number

of observations in each class. To create a frequency distribution table:

Descriptive StatisticsFrequency Distribution

Divide the results into intervals and count the number of results in each interval.

1

Make a table with separate columns for the interval numbers, the tallied results, and the frequency of results in each interval.

2

Record the number of observations in each interval with a tally mark.

3

Add the number of tally marks in each interval and record them in the Frequency column.

4

Number Tally Frequency

0 IIII 4

1 IIII I 6

2 IIII 5

3 III 3

4 II 2

25


A cumulative frequency distribution table is more detailed than a frequency distribution table.

Cumulative Frequency Distribution

To the frequency distribution table, add three more columns for the cumulative frequency, percentage, and cumulative percentage.

1

In the cumulative frequency column, the cumulative frequency of the previous row(s) is added to the current row.

2

The percentage is calculated by dividing the frequency by the total number of results and multiplying by 100.

3

The cumulative percentage is calculated similar to the cumulative frequency.4

26


For the following dataset, the cumulative frequency distribution table is given:

Cumulative Frequency Distribution (contd.)

Lower Value Upper Value FrequencyCumulative Frequency

PercentageCumulative Percentage

35 44 1 1 10 10

45 54 2 3 20 30

55 64 2 5 20 50

65 74 2 7 20 70

75 84 2 9 20 90

85 94 1 10 10 100

37, 49, 54, 91, 60, 62, 65, 77, 67, 81

27


A stem and leaf plot is used to present data in a graphical format to enable visualizing the shape of a

distribution. For example, following are the temperatures for the month of May in Fahrenheit.

To create the plot, all the tens digits are entered in the Stem column and all the units digits against

each tens digit are entered in the Leaf column.

Graphical MethodsStem and Leaf Plots

78, 81, 82, 68, 65, 59, 62, 58, 51, 62, 62, 71, 69, 64, 67, 71, 62, 65, 65, 74, 76, 87, 82, 82, 83, 79, 79, 71, 82, 77, 81

Stem Leaf

5 1 8 9

6 2 2 2 2 4 5 5 5 7 8 9

7 1 1 1 4 6 7 8 9 9

8 1 1 2 2 2 2 3 7

28


A box and whisker graph, based on medians or quartiles, is used to view the data distribution easily.

Graphical MethodsBox and Whisker Plots

12, 13, 5, 8, 9, 20, 16, 14, 14, 6, 9, 12, 12

5, 6, 8, 9, 9, 12, 12, 12, 13, 14, 14, 16, 20

Step 1: Rewrite the data in increasing order.

5, 6, 8, 9, 9, 12, 12, 12, 13, 14, 14, 16, 20

MedianLower Quartile = 8.5 Upper Quartile = 14

Step 3: Find the lower and upper quartile.

5, 6, 8, 9, 9, 12, 12, 12, 13, 14, 14, 16, 20

Median

Step 2: Find the median for the data set.

Example: The lengths of 13 fish caught in a lake are measured and recorded as follows:

29


The box and whisker graph can now be constructed.

Step 4: Draw a number line extending enough to include all the data points.

Graphical MethodsBox and Whisker Plots (contd.)

Step 5: Locate the main median, 12, using a vertical line. Locate the lower and upper quartiles (8.5 and 14) and

join them with the median by drawing boxes.

Step 6: Extend whiskers from either ends of the boxes to the smallest and largest numbers (5 and 20) in the data set.

30


Graphical MethodsBox and Whisker Plots Inference

The following inferences can be drawn from the box and

whisker plot:

Range = 20 5 = 15

The quartiles split the data into four equal parts:

Numbers less than 8.5

Numbers between 8.5 and 12

Numbers between 12 and 14

Numbers greater than 14

31


Scatter Diagrams

A scatter diagram can be used to:

understand the correlation between two variables;

examine cause-and-effect relationships; and

identify the root cause.

The five types of correlation are:

Perfect positive correlation

Moderate positive correlation

No relation

Moderate negative correlation

Perfect negative correlation

32


In perfect positive correlation, as the value of X increases, the value of Y also increases proportionally.

Scatter DiagramsPerfect Positive Correlation

Coffee Consumption in ml (X) Milk Consumption in L (Y)

300 15

350 17.5

400 20

450 22.5

500 25

550 27.5

600 30

Example: Correlation between consumption of coffee and consumption of milk

33


In moderate positive correlation, as the value of X increases, the value of Y also increases, but not in

the same proportion.

Scatter DiagramsModerate Positive Correlation

Example: Correlation between monthly salary and monthly savings

Salary (in thousands) (X) Savings (in thousands) (Y)

45 6

48 6.2

52 8

55 8.2

57 8.5

58 8.6

60 10

65 12

34


When a change in one variable has no impact on the other, there is no correlation between them.

Example: Relation between number of fresh graduates and job openings in a city

Scatter DiagramsNo Correlation

Fresh Graduates (in thousands) (X)

Job Openings (in thousands) (Y)

80 15

100 15

90 18

95 20

89 20

90 15

95 15

35


In moderate negative correlation, as the value of X increases, the value of Y decreases, but not in the

same proportion.

Scatter DiagramsModerate Negative Correlation

Example: Correlation between the price of a product and the number of units sold

Unit Price of Product (in thousands) (X)

Units Sold (Y)

30 1000

32 980

33 970

35 965

38 950

40 920

42 910

36


In perfect negative correlation, as X increases, Y decreases proportionally.

Example: Correlation between project time extension and project success

Scatter DiagramsPerfect Negative Correlation

Time Extension (in days) (X)

Project Success Probability (in percentage) (Y)

2 80

5 60

7 40

10 20

13 00

37


A histogram is similar to a bar graph, except that the data in a histogram is grouped into intervals. A

histogram is best suited for continuous data.

Example: Number of hours spent by 15 team members on a special project in a week

The table and histogram for the data are given:

Graphical MethodsHistogram

Hours spent (X)Number of Employees

(Frequency) (Y)

0 - 2 3

2 - 4 7

4 - 6 3

6 - 8 0

8 - 10 2

1.5, 1.5, 2, 3, 3, 3, 25, 3, 5, 4, 4, 4, 4.5, 5, 6, 9.5, 10

38


Normal probability plots are used to identify if a dataset is normally distributed. A normally

distributed dataset forms a straight line in a normal probability plot.

Example: The following data sample is of diameters from a drilling operation:

Step 1: Construct a cumulative frequency distribution table and calculate the mean rank probability

estimate using the formula:

Graphical MethodsNormal Probability Plots

.127, .125, .123, .123, .120, .124, .126, .122, .123, .125, .121, .123, .122, .125, .124, .122, .123, .123, .126, .121,

.124, .121, .124, .122, .126, .125, .123

Mean rank probability estimate = Cumulative frequency

(n+1) 100

Where n = sample size

39


After performing Step 1, mean rank probability estimations are calculated. The table below lists

them:

Graphical MethodsNormal Probability Plots (contd.)

X FrequencyCumulative Frequency

(Cumulative Frequency)/(n+1)

Mean Rank (%)

0.120 1 1 1/28 4

0.121 3 4 4/28 14

0.122 4 8 8/28 29

0.123 7 15 15/28 54

0.124 4 19 19/28 68

0.125 4 23 23/28 82

0.126 3 26 26/28 93

0.127 1 27 27/28 96

n = 27

40


Step 2: Plot the graph on log paper or using Minitab, a statistical software used in Six Sigma.

Graphical MethodsNormal Probability Plots (contd.)

Minitab normal probability plot instructions

1. Paste the data in any column

2. Select graph from the menu bar

3. Select probability plot

4. Select the type of the graph single

5. Click ok

6. Double click the data column

7. Click ok

Conclusion: From this graph, it can be observed that the random sample forms a straight line, and

therefore, the data is taken from a normally distributed population.

41


Measure

Topic 4Measurement System Analysis


The Measurement Systems (MS) output is used throughout the DMAIC process. An error-prone MS

leads to incorrect conclusions. Measurement System Analysis (MSA) is a technique that identifies

measurement error (variation) and its sources to reduce variation.

In MSA, the systems capability is calculated, analyzed, and interpreted using Gage Repeatability and

Reproducibility (GRR) to determine:

measurement correlation;

bias;

linearity;

percent agreement; and;

precision/tolerance (P/T).

Measurement System Analysis

43


The objectives of MSA are as follows:

Obtain information about the type of measurement variation associated with the measurement

system

Establish criteria to accept and release new measuring equipment

Compare one measurement method with another

Form basis for evaluating a method suspected of being deficient

Measurement System AnalysisObjectives

Variation in the measurement system has to be resolved to ensure correct baselines for the project objectives.!

44


Precision and Accuracy

Precision

The ability to replicate measurements time after time, consistent measurements.

It refers to the tightness of the cluster of data.

Measurement issues related to precision can be addressed through Measurement Systems Analysis.

Accuracy

Clustering of data around a known target.

It is also known as unbiased measurement.

To have a stable measurement system, focus on the accuracy first by addressing measurement issues, and get accurate results.

In statistical measurements, the terms Precision and Accuracy are the two important factors to be

considered when taking data measurements.

45


Precision vs. Accuracy

Precision

In any measurement system, precision is the degree to which repeated measurements under unchanged conditions show the same results (repeatability).

Example: Hitting a target means all the hits are closely spaced, even if they are very far from the center of the target.

Accuracy

In any measurement system, accuracy is the degree of conformity of a measured or calculated value to its actual (true) value.

Example: Accurately hitting the target means you are close to the center of the target, even if all of the marks are on different sides of the center.

Good precision and accuracy are equally important for a stable measurement system.

46


Examples of the four combinations of accuracy and precision are shown here:

Combinations of Accuracy and Precision

The darts are random across the board.

The darts are close to the target, but are not consistent.

These are not accurate, however are precise, all the darts are closer to each other.

All the darts are on the target.

a) Low accuracy Low precision

b) Low accuracy High precision

c) High accuracy Low precision

d) High accuracy High precision

47


Bias, Linearity and Stability are the three aspects of measurement system that helps in analyzing how

good the measurements are.

While performing the MSA, it is important to evaluate these along with precision and accuracy.

Bias, linearity, and stability help you understand what is causing mismatch, if any, or resulting in

inaccurate data.

Bias, Linearity, and Stability

48


Bias is a measure of the distance between the measured value and the True or Actual value. It could

be either on the positive side or the negative side.

Example: An Analog Bathroom Weighing Scale provides an adjustment screw or a dial to set it to zero

prior to weighing.

Bias

49


Linearity is a measure of consistency of bias over the range of measurement from smaller number to

higher number and vice-a-versa.

Example: If a bathroom scale is showing 2 pounds less when measuring a 100 pound person, and 5

pounds less when measuring a 150 pound person, the scale bias is said to be non-linear. The degree

of bias changes between the lower end and high end (Linearity issue).

Linearity

50


Stability refers to the ability of a measurement system to show the same values over time when

measuring the same repeatedly.

Example: Suppose the weighing scale shows one reading in the morning and other in the afternoon

for the same item, the measurement system is said to be instable.

Stability

51


Comparison of Variable and Attribute R and R

Variable R and R

To analyze measurement systems using Variable or Continuous data.

o Example: Length, Weight, Volume, Time, Temperature, etc.

Measurement system typically involves a physical gauge and can be measured.o The result of this is quantification of the

percentage of variation contributed by the measurement system.

Attribute R and R

To analyze measurement systems using Attribute or Discrete data.

o Example: Pass/Fail, Yes/No, Count, Color, Defective/Good, etc.

Measurement system typically utilizes manual or automated counting/monitoring.o The result of this is quantification of the

proportion of defective measurements, in DPMO, % Agreement or Sigma Level.

Measurement Systems Analysis (MSA) should be done for both Variable and Attribute data.

52


Gage Repeatability vs. Gage Reproducibility

Gage Repeatability

This is the variation in measurements obtained when

one operator uses the same gage for measuring

identical characteristics of the same part repeatedly.

Gage Reproducibility

This is the variation in the average of measurements

made by different operators using the same gage

when measuring identical characteristics of

the same part.

Gage Repeatability and Reproducibility are compared here.

53


Components of GRR Study

The diagram shows repeatability and

reproducibility for six different parts (16)

for two trial readings by three operators.

Difference in readings between the

operators is indicated by green and

represents reproducibility error (part 1).

Difference in readings between trials by

the same operator is indicated by red and

represents repeatability error (part 4).

54


The following should be considered while conducting GRR studies:

GRR studies should be performed over the range of expected observations.

Actual equipment should be used.

Written procedures or approved practices should be followed.

Measurement variability should be presented as is.

After GRR, measurement variability should be separated into causal components, prioritized, and

targeted for action.

Guidelines for GRR Studies

55


The following are also considered in GRR studies:

Other GRR Concepts

Bias

Distance between the sample mean value and the sample true value

Also called accuracy

Linearity

Consistency of bias over the range of the gage

Precision

Degree of repeatability or closeness of data

Smaller dispersion results in better precision

Bias = Mean Reference Value

Process Variation = 6 (std.

deviation)

Bias % = Bias

Process Variation

Linearity = |slope| Process

Variation2gage =

2repeatability +

2reproducibility

56


Measurement resolution is the smallest detectable increment that an instrument will measure or

display. The number of increments in the measurement system should extend over the full range for a

given parameter.

Examples of wrong gages being used:

A truck scale used for measuring the weight of a tea pack.

A caliper capable of measuring differences of 0.1 mm was used to show compliance with tolerance

of 0.07 mm.

Measurement Resolution

The gage must have an acceptable resolution as a pre-requisite to GRR.!57


Repeatability or Equipment Variation (EV) occurs when the same operator repeatedly measures the

same part or process, under identical conditions, with the same measurement system.

Example: A 36 km/hr pace mechanism is timed by a single operator over a distance of 100 meters on

a stop watch. Three readings are taken:

Trial 1 = 9 seconds

Trial 2 = 10 seconds

Trial 3 = 11 seconds

Assuming there is no operator error, the variation in the three readings is known as Repeatability or

Equipment Variation (EV).

Repeatability and Reproducibility

58


Reproducibility or Appraiser Variation (AV) occurs when different operators measure the same part or

process, under identical conditions, with the same measurement system.

Example: A 36 km/hour pace mechanism is timed by two operators over a distance of 100 meters on a

stop watch. Three readings are taken by each:

The variation between the readings is known as Reproducibility or Appraiser Variation.

Repeatability and Reproducibility (contd.)

Trial Operator 1 Reading Operator 2 Reading

1 9s 12s

2 10s 13s

3 11s 14s

It is important to resolve EV before resolving AV, as the other way round is counter-productive.!59


Important considerations while collecting data are as follows:

The number of operators are usually 3.

The number of units to measure is usually 10.

General sampling techniques are used to represent the population.

The number of trials for each operator is 2 to 3.

The gage is checked for calibration and resolution.

The units are measured by the first operator in random order, and the same order is followed by

the other operators.

Each trial is repeated.

Data Collection in GRR

60


ANOVA is considered the best method for analyzing GRR studies due to the following reasons:

ANOVA separates equipment and operator variation, and also provides insight on the combined

effect of the two.

ANOVA uses standard deviation instead of range as a measure of variation and therefore gives a

better estimate of the measurement system variation.

The primary concerns in using ANOVA are those of time, resources required, and cost.

ANOVA Method of Analyzing GRR Studies

61


The result of an MSA could have the following interpretations:

Interpretation of Measurement System Analysis

MSA Result

Operators are not adequately trained in using the gage

Calibrations on the gage dial are not clear

Gage needs maintenance

Gage needs redesign to be more rigid

Gaging location needs improvement

Ambiguity is present in SOPs

Reproducibility Error > Repeatability Error

Repeatability Error > Reproducibility Error

62


A sample template for Gage RR is given:

Gage RR Template

63


The results page of the data entered in the template is displayed here:

Gage RR Results Summary

64


The interpretation for the GRR results summary is as follows:

Gage RR Interpretation

Check the value of %GRR. If %GRR < 30, Gage Variation is acceptable, and thus the gage is acceptable. If %GRR > 30, the gage is not acceptable.

1

Check EV first. If EV = 0, the MS is reliable and the variation in the gage is contributed by different operators. If AV = 0, the MS is precise.

2

If EV = 0, resolve AV by providing operators with training.3

The interaction between operators and parts can also be studied under GRR using Part Variation. The trueness and precision cannot be determined in a GRR if only one gage or measurement method is evaluated as it may have an inherent bias.

!65


Measure

Topic 5Process Capability


Process Capability is how well the process can potentially run, if the

sources of variation are controlled and the process runs on target.

The Business judges its process by looking at the Process Capability,

which is a metric that reflects only the common cause variation,

assuming special causes are controlled.

There are two types of limits, Natural Process Limits and

Specification Limits. The USL and LSL will be as provided by the user.

Process Capability Analysis

USLLSL

67


The comparison between natural process limits and specification limits is presented here:

Natural Process Limits vs. Specification Limits

Natural Process Limits

Indicators of process variation

Voice of the process

Based on past performance

Real-time values

Derived from data

Consist of Upper Control Limit (UCL) and

Lower Control Limit (LCL)

Specification Limits

Targets set for the process

Voice of customer

Based on customer requirements

Intended result

Defined by the customer

Consist of Upper Specification Limit (USL)

and Lower Specification Limit (LSL)

If the limits lie within the specification limits, the process is under control. Conversely, if the specification limits lie within the control limits, the process will not meet customer requirements.!

68


Process Capability (CP) is defined as the inherent variability of a characteristic of a process or a

product. It is an indicator of the capability of a process.

Process Capability

Process capability (CP) =Upper specification limit Lower specification limit

6OR

Process capability CP =USL LSL

6

The difference between USL and LSL is also called the Specification width or Tolerance.!69


Process capability indices (Cpk) was developed to objectively measure the degree to which a process

meets or does not meet customer requirements.

To calculate Cpk, the first step is to determine if the process mean is closer to the LSL or the USL.

If the process mean is closer to LSL, Cpkl is determined.

Cpkl = X LSL

3Sigma, where X is Process Average and Sigma represents the Standard Deviation.

If the process mean is closer to USL, CpkU is determined.

CpkU =USL X

3Sigma, where X is Process Average and Sigma represents the Standard Deviation.

Process Capability Indices

! If the process mean is equidistant, either specification limit can be chosen. Cpk takes up the value of CpkU and Cpkl, depending on whichever is the lower value.70


Process Capability IndicesExample

A batch process produces high fructose corn syrup with a specification for the Dextrose Equivalent (DE) to

be between 6.00 and 6.15. The DEs are normally distributed, and a control chart shows the process is

stable. The standard deviation of the process is 0.035. The DEs from a random sample of 30 batches have a

sample mean of 6.05. Determine Cp and Cpk.

Process capability (Cp) =Upper specification limit Lower specification limit

6=6.15 6.00

6 0.035= 0.71

CpkU =(USL X)/(3Sigma)=6.15 6.05

30.035= 0.95; CpkL =

6.05 6.00

30.035= 0.48

Cpk = Min (CpkU,CpkL) = Min (0.95, 0.48) = 0.48

Q

A

71


The following interpretations need to be remembered:

A Cp value of less than 1 indicates the process is not capable. Even if Cp > 1, to ascertain if the

process really is not capable, check the Cpk value.

A Cpk value of less than 1 indicates that the process is definitely not capable but might be if Cp > 1,

and the process mean is at or near the mid-point of the tolerance range.

The Cpk value will always be less than Cp, especially as long as the process mean is not at the center

of the process tolerance range.

Non-centering can happen when the process has not understood customer expectations clearly or

the process is complete as soon as the output reaches a specific limit.

Capability Analysis - Cpk and Cp Interpretations

72


Process capability is the actual variation in the process specification. The steps in a process capability

study are:

Getting the appropriate sampling plan for the process capability studies depends on the purpose and

whether there are customer or standards requirements for the study.

For new processes, a pilot run may be used to estimate process capability.

Process Capability Studies

Plan for data collection Collect data Plot and analyze the results

1 2 3

73


The objective of a process capability study is to establish a state of control over a manufacturing

process and then to maintain control over a time period.

Objective of Process Capability Studies

Compare natural process limits with specification limits

Process limits fall within specification limits

Process spread and specification spread are approximately the same

Process limits fall outside specification limits

No action required

Adjust the process centering to bring the batch within specification limits

Reduce variability by partitioning and targeting the largest offender

74


To select a characteristic for a process capability study, it should meet the following requirements:

The characteristic should indicate a key factor in the quality of the product or process.

It should be possible to influence the value of the characteristic through process adjustments.

The operating conditions that affect the characteristic should be defined and controlled.

The characteristic to be measured may also be determined by customer requirements or industry

standards.

Process Capability StudiesIdentifying Characteristics

75


For attribute or discrete data, process capability is determined by the mean rate of non-conformity

and DPMO is the measure used. For this, the mean and standard deviation have to be defined.

Process Capability for Attribute or Discrete Data

is used for checking process capability

for constant and variable sample sizes.

Defects

is used when the sample size is

constant.

is used when the sample size is

variable.

Defectives

, , and are the equivalent of the standard deviation for continuous data.!

(1 )

;

76


The activities carried out in the measure phase are MSA, collection of data, statistical calculations,

and checking for accuracy and validity.

This is followed by a test for stability as changes cannot be made to an unstable process.

Process Stability Studies

Why does a process become unstable?

A process becomes unstable due to special causes of variation. Multiple special causes of variation lead to instability. A single special cause leads to an out-of-control condition.

Q

A

77


Variations can be due to two types of causes:

Process Stability StudiesCauses of Variation

Include the many sources of variation within a

process

Have a stable and repeatable distribution over a

period

Contribute to a state of statistical control where

the output is predictable

Special Causes of Variation (SCV)

Include factors external to and not always acting

on the process

Sporadic in nature

Contribute to instability to a process output

May result in defects and have to be eliminated

If indicated by Run charts, point to the need for

root cause analysis

Common Causes of Variation (CCV)

78


Process Stability StudiesRun Charts in Minitab

The steps to plot a Run chart in

Minitab are as follows:

First, enter the sample collected data.

Stat -> Quality Tools -> Run Charts

If p-values for any of the last 4 values

provided in the chart is less than 0.05,

the process has special causes of

variation, and the chances of the

process going unstable is high.

70

60

50

40

30

20

10

0

Number of runs about median:Expected number of runs:Longest run about median:Approx P-Value for Clustering:Approx P-Value for Mixtures:

44.0

20.5000.500

Number of runs or down:Expected number of runs:Longest run up or down:Approx P-Value for Trends:Approx P-Value for Oscillation:

33.7

30.2200.780

Sample1 2 3 4 5 6

Run Chart of Data

Dat

a

79


The causes of variation existing in a process are used to verify its normality or stability.

If special causes of variation are present in a process, process distribution changes and the output

are not stable. The process is not said to be in control.

If only common causes of variation are present in a process, the output is stable and the process is

in control.

For a stable process, the control chart data can be used to calculate the process capability indices.

Verifying Process Stability and Normality

80


Monitoring techniques refers to how well we can monitor the process capabilities. Some of the

monitoring techniques are as follows:

Statistical Process Control techniques;

Control Charts for monitoring both process capability and stability; and

Appropriate charts are used depending on the data type (attribute/discrete and

variable/continuous).

Monitoring Techniques

81


Quiz


a.

b.

c.

d.

QUIZKPOV stands for:

Key Process Output Variables

Key Performance Output Variance

Key Performance Outline Variables

Key Process Outline Variables

1

83


a.

b.

c.

d.

QUIZ

Answer: b.

Explanation: KPOV stands for Key Process Output Variables.

KPOV stands for:1

Key Process Output Variables

Key Performance Output Variance

Key Performance Outline Variables

Key Process Outline Variables

84


a.

b.

c.

d.

QUIZ The degree of conformity of a measured or calculated value to its actual (true) value is known as:

Precision

Linearity

Stability

Accuracy

2

85


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: Accuracy demonstrates the degree of conformity of measured value to its true value.

Precision

Linearity

Stability

Accuracy

The degree of conformity of a measured or calculated value to its actual (true) value is known as:2

86


a.

b.

c.

d.

QUIZ The degree to which the repeated measurements under unchanged conditions show the same results is called?

Precision

Linearity

Stability

Accuracy

3

87


a.

b.

c.

d.

QUIZ

Answer: b.

Explanation: The degree to which the repeated measurements under unchanged conditions show the same results is called Precision.

Precision

Linearity

Stability

Accuracy

The degree to which the repeated measurements under unchanged conditions show the same results is called?3

88


a.

b.

c.

d.

QUIZ When the data measured is consistently higher or lower than expected value with the same magnitude, it is called:

Precision

Linearity

Stability

Bias

4

89


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: It is the Measurement Bias that is consistently higher or lower than the expected value with the same magnitude.

Precision

Linearity

Stability

Bias

When the data measured is consistently higher or lower than expected value with the same magnitude, it is called:4

90


a.

b.

c.

d.

QUIZWhat does Linearity in Measurement Systems signify?

Linear Scale

Positive bias

Consistency of bias

Measurement errors

5

91


a.

b.

c.

d.

QUIZ

Answer: d.

Explanation: Measurements performed at smaller levels and measurements at higher levels have consistent bias over the range of measurements.

What does Linearity in Measurement Systems signify?5

Linear Scale

Positive bias

Consistency of bias

Measurement errors

92


a.

b.

c.

d.

QUIZ The sum of the squared deviations of a group of measurements from their mean, divided by the number of measurements is ________.

standard deviation

one

mean deviation

variance

6

93


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: Variance, denoted by 2, is given by 2 , that is, the sum of the squared deviations of a group of measurements from their mean, divided by the number of measurements.

standard deviation

one

mean deviation

variance

The sum of the squared deviations of a group of measurements from their mean, divided by the number of measurements is ________.6

94


a.

b.

c.

d.

QUIZ The repeatability of an RR study can be determined by examining the variation between:

the average of the individual inspectors for all parts.

part means averaged among inspectors.

the individual inspectors and comparing it to the part averages.

individual inspectors and their measurement readings.

7

95


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: Repeatability is determined by examining the variation between individual inspectors and their measurement readings.

the average of the individual inspectors for all parts.

part means averaged among inspectors.

the individual inspectors and comparing it to the part averages.

individual inspectors and their measurement readings.

The repeatability of an RR study can be determined by examining the variation between:7

96


a.

b.

c.

d.

QUIZFor attribute data, process capability:

is determined by the control limits on the applicable attribute chart.

is defined as the average proportion of nonconforming product.

is measured by counting the average nonconforming units in 25 or more samples.

cannot be determined.

8

97


a.

b.

c.

d.

QUIZ

Answer: c.

Explanation: The average proportion may be reported on a defects or defectives per million scale by multiplying the average ( , , ) by 1,000,000.

is determined by the control limits on the applicable attribute chart.

is defined as the average proportion of nonconforming product.

is measured by counting the average nonconforming units in 25 or more samples.

cannot be determined.

For attribute data, process capability:8

98


a.

b.

c.

d.

QUIZPerfect correlation is:

1+1

1:1

0

1/1

9

99


a.

b.

c.

d.

QUIZ

Answer: c.

Explanation: Perfect correlation, either positive or negative, is when a dependent variable changes equally with a change in the independent variable, and is represented by 1:1.

1+1

1:1

0

1/1

Perfect correlation is:9

100


a.

b.

c.

d.

QUIZ The variation in measurement average between operators for the same part with the same gage is called ______________.


Gage Repeatability and Reproducibility

Gage Variation

Gage Repeatability

10

101


a.

b.

c.

d.

QUIZ

Answer: b.

Explanation: Gage reproducibility is the variation in measurement when different operators use the same gage to measure identical characteristics of the same part.


Gage Repeatability and Reproducibility

Gage Variation

Gage Repeatability

The variation in measurement average between operators for the same part with the same gage is called ______________.10

102


a.

b.

c.

d.

QUIZRepeatability is also called _____________.

Appraiser Variation

Process Variation

Product Variation

Equipment Variation

11

103


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: Repeatability or Equipment Variation or EV occurs when the same operator repeatedly measures the same part or same process, under the same conditions, with the same measurement system.

Appraiser Variation

Process Variation

Product Variation

Equipment Variation

Repeatability is also called _____________.11

104


a.

b.

c.

d.

QUIZWhich of the following is not true for natural process limits?

They are based on past performance.

They are defined by the customer.

They are also called control limits.

They are indicators of process variation.

12

105


a.

b.

c.

d.

QUIZ

Answer: c.

Explanation: Natural process limits are derived from real-time values. Specification limits are defined by the customer.

They are based on past performance.

They are defined by the customer.

They are also called control limits.

They are indicators of process variation.

Which of the following is not true for natural process limits?12

106


a.

b.

c.

d.

QUIZ In process capability studies, if the process limits fall within the specification limits, what should be done next?13

Reduce variability by addressing the largest contributor of variation.

No action is required.

Stop the process.

Center the process.

107


a.

b.

c.

d.

QUIZ

Answer: c.

Explanation: If the process limits are within the specification limits, it means the process is in control, and no action is required.

Reduce variability by addressing the largest contributor of variation.

No action is required.

Stop the process.

Center the process.

In process capability studies, if the process limits fall within the specification limits, what should be done next?13

108


a.

b.

c.

d.

QUIZ Which of the following refers to the ability of a measurement system to show the same values over time when measuring the same repeatedly?14

Bias

Linearity

Process capability

Stability

109


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: Stability refers to the ability of a measurement system to show the same values over time when measuring the same repeatedly.

Bias

Linearity

Process capability

Stability

Which of the following refers to the ability of a measurement system to show the same values over time when measuring the same repeatedly?14

110


a.

b.

c.

d.

QUIZWhich of the following limits will be as provided by the user?

15

USL and LSL

Natural Specification Limit


Central Limit

111


a.

b.

c.

d.

QUIZ

Answer: b.

Explanation: The USL and LSL will be as provided by the user.

USL and LSL

Natural Specification Limit


Central Limit

Which of the following limits will be as provided by the user?15

112


a.

b.

c.

d.

QUIZ Which of the following implies that as the value of X increases, the value of Y also increases, but not in the same proportion?16





113


a.

b.

c.

d.

QUIZ

Answer: a.

Explanation: In moderate positive correlation, as the value of X increases, the value of Y also increases, but not in the same proportion.





Which of the following implies that as the value of X increases, the value of Y also increases, but not in the same proportion?16

114


a.

b.

c.

d.

QUIZ Which of the following refers to the grouping of data into mutually exclusive categories showing the number of observations in each class?17

Frequency distribution

Cumulative frequency distribution

Normal distribution

Standard distribution

115


a.

b.

c.

d.

QUIZ

Answer: b.

Explanation: Frequency distribution is the grouping of data into mutually exclusive categories showing the number of observations in each class.

Frequency distribution

Cumulative frequency distribution

Normal distribution

Standard distribution

Which of the following refers to the grouping of data into mutually exclusive categories showing the number of observations in each class?17

116


a.

b.

c.

d.

QUIZWhat is the key objective of the measure phase?

18

To improve the process

To measure the processes

To gather information on the current processes

To analyze the process

117


a.

b.

c.

d.

QUIZ

Answer: d.

Explanation: The key objective of the measure phase is to gather as much information as possible on the current processes.

To improve the process

To measure the processes

To gather information on the current processes

To analyze the process

What is the key objective of the measure phase?18

118


Process definition helps in defining the process and capture inputs and

outputs in the X-Y diagram.

Statistics refers to the science of collection, analysis, interpretation, and

presentation of data. The major types are Descriptive Statistics and

Inferential Statistics.

Precision refers to getting repeatable measurements and accuracy refers to

getting measurements closer to the actual measurement.

Process Capability is how well the process can potentially run, if the sources

of variation are controlled and process runs on target.

Summary

Here is a quick recap of what we have learned in this lesson:

119


Measures of central tendency, dispersion, and graphical methods are used

to analyze sample data.

MSA is used to calculate, analyze, and interpret a measurement system's

capability using Gage Repeatability and Reproducibility.

Variation in a process can be because of common causes and special causes

which determine the bias, linearity, stability, capability, distribution and

defects of a process.

Summary (contd.)

Here is a quick recap of what we have learned in this lesson:

120



THANK YOU

lssgb lesson3 measure

Documents